You can start by getting a Heroes of Azeroth Starter Set which contains two boosters,a Rule Book, 3 Rare Hero Cards, and a 33-card deck for one of the nine playing classes. You won't know what class you get in your box because they distribute them randomly .

Here is how to Play the game

First check out the official website and read all the rules and guides. It is very helpful and has lots of tips and hints on how to get started.
Then you'll need to get a Starter deck and some boosters packs.
Adding cards from booster packs can make for a more powerful playing deck. So it is usually a good idea to pick up a couple of booster packs when you get your Starter Deck so you can start powering up your own deck. Each booster pack usually contains 15 randomly distributed cards.

If your trying to find people to play with you can try to visit your local hobby shop and see if they hold World of Warcraft card tournaments or check the official website.